Издательство Springer, 1980, -152 pp.
The idea underlying this book is that a -comprehensive theory of computing may be developed based on the mathematics of relations. At present, research in each area of the theory of computation is pursued using whatever mathematical equipment appears most appropriate. While this may be the optimal strategy for one area taken in isolation, it is less than optimal for the field as a whole. Communication and cross-fertilization between different areas are inhibited, and it is harder to get a unified, synthetic grasp of the subject as a whole as long as its practitioners do not talk the same language.
The relevance of relational calculi to computing has long been recognized. In particular, Blikle's use of a relational calculus in [4] to compare three methods of program verification comes close to the approach which is being advocated here, and should be read in conjunction with Section 6.2 below. Nevertheless, there does not appear to have been any previous proposal to use these calculi as the basis for a really comprehensive theory.
Naturally, the specialists in the different areas of computing science would need to be convinced that relational theory provides an adequate alteative to their existing mathematical apparatus. At the present time this is not usually the case, so that it has been necessary to devote the first three chapters of the book to developing relational calculi which are suitable for computational applications. Even so, it is clear that much more work will be needed in this area.
The remainder of the book looks at various applications: two chapters deal with data types, two with questions related to programming, and the last chapter is conceed with metatheory.
To reformulate a major part of the theory of computation in relational terms would clearly be a large undertaking involving many workers and extending over a period of years. A book such as this can barely scratch the surface of such a project. Thus, as a matter of policy, I have not attempted to go into any one area in depth, or to bring the most recent advances into the discussion. Rather, I have tried to show how relational theory might be applicable to a number of different areas. The coverage aims to be representative, but is far from complete. Notable omissions are formal languages and automata (except for a hint in Chapter 6) , the theory of approximation, complexity theory, and the theory of relational data bases. (This last does not fit into the plan of the present book, but the connection is obvious, and should be explored.)
The Components of a Relational Calculus
A Comparison of Some Relational Calculi
Properties of Relators
The Extension of a Calculus
Types and Structures
Programs
Assignment and Efficiency
Metatheory
The idea underlying this book is that a -comprehensive theory of computing may be developed based on the mathematics of relations. At present, research in each area of the theory of computation is pursued using whatever mathematical equipment appears most appropriate. While this may be the optimal strategy for one area taken in isolation, it is less than optimal for the field as a whole. Communication and cross-fertilization between different areas are inhibited, and it is harder to get a unified, synthetic grasp of the subject as a whole as long as its practitioners do not talk the same language.
The relevance of relational calculi to computing has long been recognized. In particular, Blikle's use of a relational calculus in [4] to compare three methods of program verification comes close to the approach which is being advocated here, and should be read in conjunction with Section 6.2 below. Nevertheless, there does not appear to have been any previous proposal to use these calculi as the basis for a really comprehensive theory.
Naturally, the specialists in the different areas of computing science would need to be convinced that relational theory provides an adequate alteative to their existing mathematical apparatus. At the present time this is not usually the case, so that it has been necessary to devote the first three chapters of the book to developing relational calculi which are suitable for computational applications. Even so, it is clear that much more work will be needed in this area.
The remainder of the book looks at various applications: two chapters deal with data types, two with questions related to programming, and the last chapter is conceed with metatheory.
To reformulate a major part of the theory of computation in relational terms would clearly be a large undertaking involving many workers and extending over a period of years. A book such as this can barely scratch the surface of such a project. Thus, as a matter of policy, I have not attempted to go into any one area in depth, or to bring the most recent advances into the discussion. Rather, I have tried to show how relational theory might be applicable to a number of different areas. The coverage aims to be representative, but is far from complete. Notable omissions are formal languages and automata (except for a hint in Chapter 6) , the theory of approximation, complexity theory, and the theory of relational data bases. (This last does not fit into the plan of the present book, but the connection is obvious, and should be explored.)
The Components of a Relational Calculus
A Comparison of Some Relational Calculi
Properties of Relators
The Extension of a Calculus
Types and Structures
Programs
Assignment and Efficiency
Metatheory